Movie 43 is a basic comedy shtick driven movie that seems to be directed at the humor level that teenage boys are supposed to have. It's not an entirely new type of movie following pretty much the basic premise of the Scary Movie's, Epic movie, "Making-fun-of-genres" movies that are out there today. However one of the biggest selling points for this movie as well as the main reason many will go see it is the many big name stars that are appearing in this movie. So how did this movie get so many big stars to act in it?

2 Answers
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In short most of them are Wessler's friend and second its due to Wessler's attitude of “Wait for them. Shoot when they want to shoot. Guilt them to death.”

For long read the below mentioned Wikipedia summary

It took years for Wessler to recruit his actors for the film. He says
that he was turned down plenty of times because all the actors were
asked to work for scale.

He says. “The truth is, I had a lot of
friends who were in this movie. And if they didn’t say yes, this movie
wouldn’t have gotten made." In end, most of the actors were willing to
take part because the film only required a few days of their time and
often allowed them to play a character outside of their wheelhouse.

Hugh Jackman was the first actor Wessler cast. He met the star at a
wedding and then called him some time later and pitched him the short.
The actor read the script and agreed to be a part of the film. “He
called me back I think 24 hours later and said, ‘Yeah I wanna do
this,’ which I think is, quite frankly, incredibly ballsy. Because you
could be made a fool of, or you could look silly, and there will be
people who say, 'That’s crazy; he should never have done it."

After talking to the multiple agents of Kate Winslet, she eventually
agreed to take part. The Winslet-Jackman sketch, that was shot shortly
after, became the reel to attract other A-list stars.

John Hodgman, who plays opposite Justin Long in one sketch, signed on
with no knowledge of the project. Hodgman said, “I got an e-mail from
Justin that said, ‘I’m going to be dressing up as Robin again. Do you
want to dress up as the Penguin?’ And I said yes. Without even
realizing cameras would be involved, or that it would be a movie.
Justin is one of the funniest people on earth.”

Richard Gere, said yes — though he wouldn’t be available for more than a year. So Wessler
waited him out. He thought the idea of his sketch was too good. Gere
eventually called Wessler and told him he was free to shoot, on just a
couple of conditions: They had to do it in four days, and they needed
to relocate the shoot from Los Angeles to New York.

It didn’t work on everyone. Colin Farrell initially agreed to be in
the Butler leprechaun sketch — as Butler’s brother, also a leprechaun
— but then he backed out and Gerard Butler did the sketch by himself.

Farrelly says that when he approached George Clooney about playing
himself in a sketch (the gag was that Clooney is bad at picking up
women), Clooney told him “No fucking way.” There was to be a sketch
directed by Bob Odenkirk that starred Anton Yelchin as a necrophiliac
who worked at a morgue and had sex with the dead female bodies that
was shown at a test screening of the film, but was cut out of the
final film. Producer John Penotti said that the sketch will be seen on
the DVD and Blu-ray of the film.(Source: Wikipedia)

...it did take a few years because of the way Charlie Wessler produced it along with John Penotti and myself and from the beginning, they knew the only way to do this was to be able to work with the actor's schedules.

So in other words, when they call someone like Kate Winslet and Hugh Jackman and say, "Hey, would you want to do a short in this compilation film?" They might say, "Yeah, I'd love to but I can't do it for a year and a half" then they'd say, "Okay, we'll wait."

That's how we did it. We had all different crews, all different directors so it was easier to just shut down so we'd go sometimes a year without shooting one and then you'd do like three or four and then you'd wait six months and do a couple more. That's how we did it.

Charlie Wessler is one of these guys, he's a bit of a Gatsby-like character because you might not have heard his name but everybody in Hollywood knows him.

It's weird. He knows everybody. You'd be sitting in a room and no matter who comes up, he's like "Yeah, I worked with that guy." "What?! What do you mean you used to work with them?" He was a P.A. on "Star Wars" and over the years, he's gotten to know everybody so pretty much everybody in the movie were acquaintances of his that he could just call personally and say "Hey, listen do you want to do this thing? It's only going to take you one day." And they'd be like, "Yeah, sure Charlie, I'll do that."